On the use of case estimate and transactional payment data in neural networks for individual loss reserving

TL;DR

It is found that case estimates will improve predictions significantly, but that equipping the neural network with memory only leads to meagre improvements, and a standardised methodology for assessing their value is provided.

Abstract

The use of neural networks trained on individual claims data has become increasingly popular in the actuarial reserving literature. We consider how to best input historical payment data in neural network models. Additionally, case estimates are also available in the format of a time series, and we extend our analysis to assessing their predictive power. In this paper, we compare a feed-forward neural network trained on summarised transactions to a recurrent neural network equipped to analyse a claim's entire payment history and/or case estimate development history. We draw conclusions from training and comparing the performance of the models on multiple, comparable highly complex datasets simulated from SPLICE (Avanzi, Taylor and Wang, 2023). We find evidence that case estimates will improve predictions significantly, but that equipping the neural network with memory only leads to meagre improvements. Although the case estimation process and quality will vary significantly between insurers, we provide a standardised methodology for assessing their value.

Figures (14)

• Figure 1: Architecture of FNN and FNN+ models (as will be defined in Section \ref{['sec:inputs']}). The yellow node (case estimate summaries) is included in the FNN+ and excluded from the FNN. All inputs are static.
• Figure 2: Architecture of LSTM and LSTM+ models (as will be defined in Section \ref{['sec:inputs']}). The yellow node (case estimate) is included in the LSTM+ and excluded from the LSTM. The inputs to the recurrent layer(s) are time series, while the remaining inputs are static.
• Figure 3: Example of an unrolled RNN.
• Figure 4: Boxplots showing the aggregate predictions of outstanding claim amounts (expressed as a proportion of the true amounts outstanding) and $\text{vsCE}_{\text{OCL}}$ for the LSTM+ and FNN+ at the valuation date, subset by quarters since notification. The black curves represent the proportion of the actual amounts outstanding related to predictions made on or before quarter q. Stronger performance is indicated by values closer to 1 for \ref{['fig:LSTM+_FNN+_OCLs_dev']} and larger values for \ref{['fig:LSTM+_FNN+_vsCE_OCL_dev']}.
• Figure 5: Boxplots containing MALE, MSLE, reserve error and $\text{vsCE}_{\text{OCL}}$ metrics for the LSTM+ and FNN+ at the valuation date. Smaller values for \ref{['fig:LSTM+_FNN+_MALE_val']} and \ref{['fig:LSTM+_FNN+_MSLE_val']}, values closer to 0 for \ref{['fig:LSTM+_FNN+_OCLs_val']} and larger values for \ref{['fig:LSTM+_FNN+_vsCE_OCL_val']} indicate stronger performance.